Finally I could take some time to work on the project. I improved the power grid to have the smallest number of  "steps" between the power supply and each IC, and suddenly everithing works just fine, not having the issues I reported in the last log entry anymore. Even some leds looks brighter right now.

The IC 74ALS874 (8 bit register) seems to be the more sensible to lower voltages. Maybe it's common to the ALS family.

The E register is almost working (bottom right), hope I could finish it today and make arithmatic operations between the A and E registers soon.

As a small note: I'm using a cheap USB ampmeter in the power supply (like this one) so I can know the current all the time (picture below). It is useful for debugging too, when you misconnect some wire and short circuit some component, the circuit frequently still works, but it's draining a lot more current. In my case it showed a rise from the normal 200mA to more than 700mA, and I could shut off imediatelly and revise the connections before to fry some IC.

Thanks for reading.